Vice President Bill Clinton?
While Bill Clinton cannot be elected to a third term as President, there is nothing prohibiting him from serving as President or serving as Vice President, Speaker of the House of Representatives, or any of the other positions that would put him a hearbeat away from the presidency. To wit, upon the incapacity, death, resignation, or removal from office of the sitting President, Vice President Bill Clinton would be sworn in. Moreoover, if the President-elect were to die before being sworn in, Vice President-elect Bill Clinton would become President on Inauguration Day.
The Twelfth Amendment states, in pertinent part, that "no person constitutionally ineligible to the Office of President shall be eligible to that of Vice-President of the United States." However, when the Twelfth Amendment was ratified, Presidents were not subject to term limits, and they did not have vice-presidential running mates. According to the original provisions of Article Two, the only way to become elected Vice President was to run for President and come in second place. Running mates were an invention of the Electoral College that grew out of the Twelfth Amendment's requirements that separate votes be cast for President and Vice President by the members of the college.
After Franklin Delano Roosevelt was elected to an unprecedented four terms as President, the Twenty-second Amendment was ratified, providing that "No person shall be elected to the office of the President more than twice, and no person who has held the office of President, or acted as President, for more than two years of a term to which some other person was elected President shall be elected to the office of the President more than once." As recently as 1964, there was talk of then former President Dwight D. Eisenhower running for Vice President as Barry Goldwater's Republican running mate after Eisenhower had already been elected twice to the presidency. And then in 2004, some people suggested that John Kerry might ask Bill Clinton to be his running mate. Stranger things have happened.